Clock Based tips

Aptitude problems based on clocks can be generally 2 types

1. Angle based problems
2. Incorrect clocks

Basic rules:

For Angle based problems:

• Every hour, Hour hand and minute hand co-incides only once
• Every minute, seconds hand and minutes hand coincides only once
• Angle traced by hour hand in 12 hrs = 360°
• Angle traced by minute hand in 60 min. = 360°.
• In every 60 minutes,  Minute hand gains 55 minutes on hour hand.

Power of 22:

• Two right angles per hour(Right angle = 90, Straight angle=180)
• Forty-four right angles per day
• Between every two hours, the hands of the clock coincide with each other for one time except between 11, 12 and 12, 1.In a day they coincide for 22 times.
• Between every two hours, they are perpendicular to each other two times except between 2, 3 and 3, 4 and 8, 9 and 9, 10.In a day they will be perpendicular for 44 times.
• Between every two hours, they will be opposite to each other one time except between 5, 6 and 6, 7.In a day they will be opposite for 22 times.

Speed:

1. Speed of the hour hand     = 0.5 degrees per minute (dpm)
2. Speed of the minute hand  = 6 dpm
3. At ‘n’ o’ clock, the angle of the hour hand from the vertical is 30n

          For Incorrectness based problems:

If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast

 if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow

Usually, there are few formats you need to consider before solving:

1. 24 hr format: 00:00 - 23:59.
2. 12 hr format: 00:00-11:59 AM ,00:00 to 11:59 PM.
3. Military format 0000-2359.

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Example problems:

Angle based problems:

Example : 1  

What is the angle between hours hand and minutes hand at 7:20?

solution: 1

At 7 -0 clock, Angle between hours hand and vertical =(Angle made by vertical and hours hand up to 7)+(Extra angle traced from 7 to 7:20)

Angle(H)=7*30°+(0.5*20)°  {Hours hand moves 0.5 degrees/minute}

Angle(H)=210°+10°=220°

Angle(Minutes hand)=20*60°=120°

Angle(H)-Angle(M)=220°-120°=100°

solution: 2

Using formula:

  Angle between X and Y =|(X*30)-((Y*11)/2)|

1. X=7 Y=20
2. Angle= (7*30)-((20*11)/2)
3. Angle=210°-110°
4. Angle=110°

Example: 1  

How many times do hours hand and minutes coincide in a day?

solution: 

22 Times,

For every 1 hr, it coincides once but in case of 11, it coincides after 11:59 which is 12:00

Example: 2

At what time in between 9 and 10, both the hands intersect?

solution:

At the time of Intersection, the angle will become zero.

and Hour's hand will definitely represent 9(As it intersects somewhere between 9:00 - 9:59)

to calculate minutes, we apply the formula

  Angle between X and Y =|(X*30)-((Y*11)/2)|

0=(9*30)-(Y*11)/2

9*30=Y*11/2

Y=(9*30*2)/11

Y=49.0909

Hence both the hands intersect at 9 hours 49 minutes 0.09*60=6 seconds

Problems based on Incorrectness:

Example :

A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?

solution:

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

If you have any other problems or solutions, please let us know :)

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